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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 133200.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
133200.g1 | 133200ee2 | \([0, 0, 0, -49275, -3705750]\) | \(10503459/1369\) | \(1724545728000000\) | \([2]\) | \(786432\) | \(1.6520\) | |
133200.g2 | 133200ee1 | \([0, 0, 0, 4725, -303750]\) | \(9261/37\) | \(-46609344000000\) | \([2]\) | \(393216\) | \(1.3054\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 133200.g have rank \(1\).
Complex multiplication
The elliptic curves in class 133200.g do not have complex multiplication.Modular form 133200.2.a.g
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.